[en] According to current evolutionary scenarios, neutron stars in Low Mass X-Ray Binaries (LMXRBs) are spun-up by accretion torques to limiting periods in the millisecond range and give rise to 'recycled' millisecond radio pulsars once accretion stops^1-3. In addition to persistent sources, the X-ray sky is populated by a number of transient sources. Among them, Soft X-Ray Transients (SXRTs), when in outburst, show properties similar to those of LMXRBs^4-6. SXRTs are characterised by luminosities, and therefore mass accretion rates, that vary over many decades: while it is clear that when in outburst their emission is powered by accretion onto the neutron star surface, the origin of the low-level emission detected during quiescence remained uncertain^7,8. Here we report on BeppoSAX pointed observations of Aql X-1, the first to follow the decay of a SXRT outburst down to quiescence. The fast X-ray flux decay that leads to quiescence is most readily interpreted in terms of the propeller effect arising from the very fast rotation of the neutron star magnetosphere. The hard X-ray spectrum that characterises the quiescent emission is probably due to shock emission powered by a turned-on radio pulsar